CHICAGO — “America’s Founding Myth” might have been a catchier title for Ric Burns’ new film “The Pilgrims,” which explores the crossing of the Mayflower and settlement in the so-called New World in 1620.

But even that would do too little service to the harrowing story of how a band of English separatists came to unite with a Native American tribe, opening the way to a British foothold in North America.

Like much of history, which is often smoothed of its rough edges and boiled down for school children to a few symbols — buckled shoes, Indian corn — the whole truth is not only ugly but far more fascinating than any of our textbooks ever hinted at.

Burns — best known for award-winning documentary films about Andy Warhol, Eugene O’Neill and Ansel Adams — takes us straight into the heart of the Pilgrim experience through the writings of William Bradford, a founding governor of Plymouth Colony and its official historian.

Through Bradford’s life story, we trace the origins of the separatist Protestants who first fled Scrooby, England, to Leiden, Holland, in order to get away from a Church of England they felt was corrupt and inhibited their direct spiritual connection to God.

From there, we visit the depths of humans’ capacity for misery, first through a terrifying, two-month trip on the Mayflower, an off-course landing on a mass Native American grave and then through a first winter that saw half of the small group of Pilgrims die of illness, harsh conditions and starvation.

Thus their nightmare began.

Rather than finding a heaven on earth, they were faced not only with physical hardships but with the necessity of turning their backs on some of their own religious principles in order to survive.

These Pilgrims’ relationship with the indigenous population was complex — neither as bad as the worst retellings of colonialist terror, nor as good as our founding legends have always suggested.

Faced with a variety of native peoples seeking to defend their territory, the Pilgrims turned first to propping up their dead in the forests to make it look as though they had muscle to protect themselves. Then they formed an alliance with the Wampanoag tribe, which had been decimated earlier by a plague brought to their land by European fisherman.

These two groups were so vulnerable to attacks from other tribes that they had little choice but to band together — even to the point of mounting the head of a decapitated native person at the entrance of their settlement to send a clear message that they would not be driven off from their new home.

Burns punctuates his gorgeous cinematography — the Mayflower II, the only full-scale replica of the Pilgrims’ vessel in existence, was taken out onto the Atlantic to recreate some of the voyage — with pointed, difficult questions about why we, as a country, have come to think about the Pilgrims and the first Thanksgiving the way we do.

“The way we choose to remember this tells us more about what we wish ourselves to be than who we really are. When you’re done looking at the full story with a little more context, you realize that we needed a founding myth in order to forget our slaveholding past,” Burns told me, referring to Lincoln’s proclamation of Thanksgiving as a national holiday during the Civil War. “Downplaying Jamestown, which was founded in 1607, involves a willed cultural amnesia that points to Americans’ desire to think of ourselves as people who broke bread with Native Americans instead of as slaveholders.”

None of the historians — English, American and Native American — who help bring this story to life pull any punches in their analysis of how poorly the settlers’ first contact with Native Americans went for all involved. Bradford himself wrote that when the separatists who stayed behind in England learned of the decapitated head on display, one former leader wrote back shamed, lamenting that it would have been better to convert the natives than to kill them.

Viewers who appreciate an unvarnished look at history and thoughtful conversations about how the past informs our present will find “The Pilgrims” refreshing. It puts the awfulness of the pilgrims’ and Native Americans’ fraught relationship into a context that encourages self-reflection rather than finger-pointing.

“The Pilgrims” premiered on Tuesday on PBS and will air again on Thanksgiving Day.